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Thinkport | Probability and Tree Diagrams

Use a tree diagram to find the probability that a set of triplets will be all girls in this interactive from MPT. In the accompanying classroom activity, students find the probability of various outcomes of compound events involving a set of dice, such as the probability of rolling doubles and the probability of rolling at least one “2.” They share solution strategies, including methods of representing sample spaces for these compound events. To get the most from the lesson, students should have experience developing and using uniform probability models. For a longer self-paced student tutorial using this media, see "Tree Diagrams" on Thinkport from Maryland Public Television.

Materials: Per student: pencils; Roll Two Dice worksheet; per pair: two dice, each a different color

Procedure1. Introduction and Interactive (10 minutes, whole group and pairs) Engage the class in discussing gender of twins and triplets whom they know. In the course of the discussion, establish that the theoretical probability of each outcome, boy or girl, is 1/2. That is, the sample space consists of two possibilities: 1/2 chance of a girl, and 1/2 chance of a boy.

Ask students to discuss the following problems with a partner: What is the probability that twins will both be girls? That triplets will be all girls?

After a few minutes, call the class together and explain that they will see one way to find the solution.

Launch the interactive and work through it with the class, with the following modifications:

Screen 1. Introduce the term tree diagram.

Screen 2. After you click on the tree diagram, ask, What is the probability of two girls? A girl and a boy? How do you know?

Screen 5. After you click on the tree diagram, establish that there are eight possible outcomes (considering birth order). Give pairs a moment to revisit their answers for the probability of three girls before continuing on to reveal the answer.

Screen 7. Ask pairs to talk over the probability of a boy and two girls (in any order), and at least one boy (in any order).

2. Uniform Probability with Dice (10–15 minutes, pairs) Distribute the materials. If students are unfamiliar with dice, give them a few minutes to investigate the number of faces and what the faces display. Check that students understand they have an equal chance (1/6) of rolling each number.

Review the worksheet instructions, emphasizing that students record their thinking with diagrams or charts. Explain that they may use the dice to help think through possible outcomes.

Circulate to encourage students having difficulty to represent the possible outcomes with a tree diagram, and to ask questions such as:

Wrap up by asking students to reflect on ways to represent sample spaces:

How do tree diagrams help you figure out probabilities?

What other approaches did you find helpful?

Activity Extension: Have students answer the following problem: Imagine you are rolling two dice and finding the sum of your rolls. What sums do you have the greatest probability of rolling? How do you know? What is the probability?